Answer: Yes we conclude that both teachers are effective.
Step-by-step explanation:
Null Hypothesis, :
=
{ It means both teachers are equally effective}
Alternate Hypothesis, :
<
or
The test statistics here we use is :
~
So now we will indicate each and every expression in the above test statistics,
is the average test score of Mrs. smith's students = 78
is the average test score of Mrs. Jones' students = 85
Formula for =
,where
= 10 and
= 15
= 30 and
= 25
putting values in , we get
Now solving Test Statistics = follows
= -2.0656 follows
From the t table at 5% level of significance we know that our level of significance will lie between degree freedom 40 and 50 which is 1.684 to 1.671 and our test statistics is way more than this,
Hence we have do not have sufficient evidence to reject null hypothesis and we conclude that both teachers are equally effective.